Metacognition as Remediation of Dyscalculia and Obsessive Compulsive Disorder

Abstract

Academic success is an important component in the life of young children and will impact future employment opportunities. Meeting with academic success and being prepared for today's rapidly changing workforce depends upon students being able to develop skills to direct their own learning. Since 1980, educators have recognized the importance of providing curriculum that encourages thinking skills rather than simply providing students with factual knowledge that is likely to become increasingly obsolete with today's expanding technology industry (Collins-Block, 1993). Learning mathematics is becoming a necessity in a modern society; the societal expectancies, as appears on school curriculums, are higher, and the learning difficulties are more obvious. The overall prognosis for mathematics achievement for students with LD as they finish school is not optimistic. Lack of achievement in mathematics is growing global as well as national concern and it is likely that there will be an internal emphasis on mathematics instruction for the new future, for learning disabled students. In fact mathematics is a way to settle in mind a habit of reasoning so the question arises, “How do we do mathematics in our heads” this question is related to the issues such as children’s acquisition of arithmetic knowledge and skills and nature of arithmetic problems in children with dyscalculia. Metacognitive strategies positively impact students who have learning problems because they provide these students an efficient way to acquire, store, and express information and skills (Mercer & Mercer, 1993). However, little is known about the nature of elementary student’s use of metacognitive strategies, and how these strategies are applied when students solve problems.

The identification and description of LD began in the western world in the 1950s and 60s. The major developments of the LD movement during this period centered on children, who appeared normal in many intellectual skills but displayed a variety of cognitive limitations that seemed to interfere with their ability to read, write and learn in the classroom. These were essentially deficient general learning processes centering mostly on what we today call distractibility, hyperactivity and visual-perceptual and perceptual-motor problems.

Individual differences among learners across all stages of learning have clearly revealed the presence of recreation, innovation, and giftedness among learners. Moreover, a large amount of evidence indicates dysfunction and disabilities among learners in different grades. The learners with learning disabilities become one of the groups receiving the most attention, particularly after including students not suffering from clear disabilities such as blindness, deafness, or any other mental or physical disability (Barratt, 2008). Additionally, the number of learners classified with disabilities is increasing continuously, making them the most representative class of learners with special needs (Heward, 2006).

The LD movement in India is of more recent origin and comparable today with that of the western LD movement of nearly half a century ago. In the eastern world, LD was earlier considered a problem of English speaking countries. The apparent lower incidence of these types of difficulties resulted in a relative lack of concern about LD in Asian countries such as India and China. Reports of lower incidences of LD in the eastern world were attributed by Western scholars to the general lack of awareness and sensitivity among educationists. The specific difficulties faced by children learning to read were attributed to the overcrowded classrooms. At the same time, reports of the high incidence of problems associated with the acquisition of reading in Western countries was attributed by easterners to the vagaries and complex nature of alphabetic writing systems such as English (Karanth, 2002).

Ironically, policy related to learning disability is yet to see the daylight. In absence of such a policy and incongruous environment, children with LD cannot be rehabilitated in regular schools. Though isolating such children from regular schools for training at special schools is not a good precedent, it is the best available option in the prevailing conditions and inevitable too. During the last decade or two, however, there has been an increasing awareness and identification of children with LD in India. Despite this growing interest, we still have no clear idea about the incidence and prevalence of LD in India.

Concept of Learning Disabilities

Learning disabilities can affect a person's ability in the areas of listening, speaking, reading writing and mathematics and is often first suspected when there is a clear and unexplained gap between an individual's level of expected and actual levels of achievement. Learning disabilities also can encompass problems in the area of social-emotional skills and behaviour, and some individuals with learning disabilities struggle with peer relationships and social interactions in addition to academic challenges. According to the National Center for Learning Disabilities, LD is a neurological disorder that affects the brain's ability to receive process, store and respond to information. The term learning disability is used to describe the seeming unexplained difficulty a person of at least average intelligence has in acquiring basic academic skills. These skills are essential for success at school and at workplace and for coping with life in general. LD is not a single disorder. It is a term that refers to a group of disorders in listening, speaking, reading, writing and mathematics.

Learning Disabilities refer to a number of disorders that interfere with a person’s ability to store, process or produce verbal or non verbal information. These disabilities are distinct from and not caused by limited intellectual functioning or sensory, psychiatric, or motor disabilities.Learning disability is not being diagnosed on the basis of a predictable set of symptoms. Rather, LD is a broad term that covers a pool of possible causes, symptoms, treatments, and outcomes. The main indicator of LD is a significant difference between the expected ability of an individual and his/her performance. Even though a person’s IQ may be in the normal range, his/her achievement in a specific area may be well below normal. Discrepancy refers to a difference between ability and achievement. A student with a learning disability may seem quite capable of learning but have unexpected difficulty in one or more of the academic areas.

Learning Disabilities is one of the important causes of poor academic performance in school-going children. These are developmental disorders that usually manifest during the period of normal education. These disabilities create a significant gap between the true potential and day-to-day performance of an individual. Learning disabilities range in severity and may interfere with the acquisition and use of one or more of the following:

· Oral Language · Reading · Written Language · Mathematics

Learning Disabilities is a term within whose scope lie a number of disabilities. Often, a child displays a combination of these disabilities. The inherent complexities of the notion of LD are further complicated by an acute lack of teacher awareness, of clear-cut assessment procedures or indigenous tools for assessment of processing deficits, intelligence testing and testing for proficiency in reading and writing (Karanth, 2002).

Dyscalculia

In the modern world, mastery over basic academic skills- reading, writing and arithmetic is a necessary pre-requisite for success in all walks of life. Infact, numeracy and literacy form the fundamental skills needed for effective citizenship in a knowledge-based society. These skills are the basic for an individual to realize their potentialities. Impairments of skills in these areas among children, which occur despite appropriate levels of intelligence and opportunities to learn, are termed as specific learning disabilities.

There are a great number of students who have serious difficulties in learning mathematics, but find the rest of academic subjects easy. These students have high IQs, are excellent readers, creative writers and learn quickly. But when it comes to any subject that requires understanding and application of the language of mathematics, they fail miserably (Newman, 1998). In fact, mathematics is the very base of human civilization as everything we do in our daily life is governed by maths. It provides pupils with powerful ways of exploring, investigating and understanding the world. It is a subject that consists of two aspects: · Knowledge: There is much in math that one simply has to know and therefore, has to learn, e.g., many terms, definitions, symbols, theorems and axioms. · Skills: On the other hand, there are many things in mathematics that the learner must learn to do, e.g., the skills of counting, adding & subtracting, multiplication and division. Furthermore, one of the most important skills for math is logical thinking, which makes problem solving possible.

Dyscalculia is a specific learning disability that is characterized by an impaired ability to learn about and process numerical and mathematical information that is not attributed to general intellectual disabilities (American Psychiatric Association, 2013). A number of studies have shown that Mathematical Learning Disabilities children exhibit poorer Word Problem Solving abilities than do their typical peers (Montague, 2008; Geary, 2011; Bryant, et. al. 2000) and that they are typically poor mathematical problem solvers with restricted cognitive and metacognitive knowledge (Rosenzweig et. al., 2011; Gonzalez et. al., 2002; Montague & Applegate, 1993).

Dyscalculia is an inability to conceptualize numbers, number relationships (arithmetical facts) and the outcome of numerical operations estimating the answer to numerical problems before actually calculating. (Sharma, 1997) Dyscalculia is not a term intended to be used for anyone who is poor at maths. What we have to find is that there are some children whose ability to handle mathematical concepts is significantly lower than we might expect to be, when taking into account individual’s age and intelligence. All mathematics teachers have encountered children with dyscalculia. However few teachers are aware of causes of their problems and very few of them are able to recognize and deal with problem of dyscalculia.

Concept of Metacognition

Metacognition is probably the most actively investigated cognitive process in contemporary research in developmental and instructional psychology (Tobias et al. 1999) Metacognition is a form of cognition, a second or higher order thinking process which involves active control over cognitive processes. It can be simply defined as thinking about thinking or as a “person’s cognition about cognition” (Wellman, 1985). Metacognition is a concept of cognitive psychology that “focuses on the active participation of the individual in his or her thinking process” (Stewart & Landine, 1995). The term metacognition first appeared around 1975 in the work of developmental psychologist John Flavell from Stanford University. He used the term to denote:

“One’s knowledge concerning one’s own cognitive processes and products or anything related to them (...) [and] refers, among other things, to the active monitoring and consequent regulation and orchestration of these processes (...), usually in the service of some concrete goal or objective” (Flavell,1976). This definition emphasizes the executive role of metacognition in the regulation of cognitive processes. Executive processes are those responsible for the goal-directed processing of information and selection of action, and for the implementation and monitoring of task-specific cognitive processes. The ‘meta’ refers to higher-order cognition about cognition, or ‘thinking about one’s thinking’. It is often considered to have two dimensions: metacognitive knowledge and metacognitive regulation. Metacognitive knowledge includes the learner’s knowledge of their own cognitive abilities (e.g., I have trouble remembering people’s names), the learner’s knowledge of particular tasks (e.g., the ideas in this article are complex), and the learner’s knowledge of different strategies including when to use these strategies (e.g., if I break telephone numbers into chunks I will remember them) (Brown, 1987; Flavell, 1979). Metacognitive regulation describes how learners monitor and control their cognitive processes. For example, realising that the strategy you are using to solve a maths problem is not working and trying another approach (Nelson & Narens, 1990).

Metacognition is considered a critical component of successful learning. It involves self-regulation and self-reflection of strengths, weaknesses, and the types of strategies you create. It is a necessary foundation in culturally intelligent leadership because it underlines how you think through a problem or situation and the strategies you create to address the situation or problem. A person is said to be metacognitively developed when he/she know his /her strengths as well as weaknesses and the processes that are used to overcome the weaknesses. This is the tool to help students with Learning Disabilities in problem solving processes.

Metacognitive Strategies as Remediation for Dyscalculia

A good understanding of mathematics is necessary not only for academics also for a fundamental skill which is required in a person’s personal, social, and work life. Mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. However, nowadays Indian students underperform in mathematics. As per the Seventh Annual Survey of Education Report (ASER), 2012, of rural India, school enrolment has risen but there is a decline in attendance, over-reliance on private tuitions and decline in reading and mathematical ability of children in the age group between 6 and 14. In order to improve performance in mathematics and ensure that our students are equipped with the mathematical skills needed to succeed in a global marketplace, there is a need to start from the basics at primary level. The major reason for the difficulty in comprehending mathematical concepts is their abstract nature and lack of multi step problem solving skill. Thus, use of innovative techniques which make the mathematical concepts concrete and help in memorizing the basics along with inculcation of basic mathematical concepts and skills could be useful in improving the mathematical ability.

As our children go about their daily lives exploring and discovering things around. Then they exposed to the world of mathematics. In fact the word is filled with numbers, symbols, manipulations, problem solving, conceptualize, processing and reasoning, so how does one survive who has a learning disability in area of mathematics? Mathematics is a major skill area. Students experience failure in arithmetic often lack basic skills like conceptual understanding, counting, sequence, procedural steps of computation, application of arithmetic skills, and problem solving. The overall prognosis for mathematics achievement for students with learning disability as they finish school is not optimistic. Cohn (1968) explains that failure in maths is socially expectable. Math ability is more regarded on a specialized intellectual function, rather than a general indicator if intelligence.

According to the DSM-IV, developmental dyscalculia is a rare learning disability, with a prevalence of 1% in the school-age population (American Psychiatric Association, 1994). Population studies for the United States, Europe, and Israel demonstrate that the prevalence of developmental dyscalculia in these countries is similar, ranging from 3%-6.5% (Gross-Tsur et. al 1996; Badian N. A., 1983; Lewis, C. et. al., 1994; Hein, J. 1999). However, it is estimated in the literature that 5–10% of school children have learning disabilities indifferent levels and characteristics, which affect the learning in math (Mazzocco and Thompson 2005). Professor Brian Butterworth proposes that the current (2001) best estimates indicate a prevalence of between 3% and 6% of the population. These estimates are derived from the proportion of children who have special difficulty with maths despite good performance in other curriculum areas.

For many children, mathematics is an inherently difficult subject to learn. Between 5 and 8 percent of children between the ages of 6 and 14 have a particular type of cognitive deficiency that limits their aptitude to acquire knowledge and understanding of fundamental ideas in numeracy (Geary, 2004). Increasingly, researchers in the cognitive sciences are studying this deficiency under the name dyscalculia, a disorder in which normally intelligent children demonstrate specific disabilities in learning mathematics (Ansari & Karmiloff-Smith, 2002).

Remediation is a process of leading to the correction of difficulties and weakness in performance in this process the individual is provided instruction, begning at child’s level and progressing forward at the rate at which the child is able to learn. Remediation of dyscalculia is based on certain principles which are applicable to all type of mathematical learning and essential for effective teaching and remediation. The principles which have been followd in development of material for learning disabled include number concept, teaching from concrete to abstract, providing opportunities and time for practice, generalizing the concept and the skill that have been learned, work with student strengths and weaknesses building a solid foundations of mathematic concepts and skillsand providing a balanced mathematics programme. But for the teacher before developing the marterial for instructing the children with dyscalculia, it is necessary for him/ her to have the knowledge of subject as well as the weakness and strength of the students.

Proponents of current efforts to reform mathematics education believe that if quality of instruction is to be impaired, the eduacters will have to dramatically change their perspective on how mathematics should be tought. The teachers must have at hand effective instructional procedures, materials and other resources to teach mathematics to students with learning disabilities based on assumption that all students can learn.

The movement toward inclusive education for children with disabilities is now gaining strength and it has become increasingly important to understand how general education teachers perceive the academic outcomes of these children. The largest groups of children with disabilities in special education programs are those with learning disabilities. Learning disability is a complex phenomenon to understand. There are many connotations of learning disabilities thus even today it creates confusion in the mind of the general public and the professionals. Learning disability is a disorder in one or more of the basic psychological processes involved in understanding of spoken or written language. These may be manifested in disorders of listening, thinking, talking, reading, writing, spelling or arithmetic.

However, it is estimated in the literature that 5–10% of school children have learning disabilities in different levels and characteristics, which affect the learning in math (Mazzocco and Thompson, 2005). According to the cognitive approach, the characteristics of the disability are clearly related to learning difficulties in math. Visual processing, visual memory, and space awareness affect the acquiring of math skills, because they are significant parts of acquiring mathematical knowledge that includes conceptual knowledge and procedural knowledge (Kilpatrick et al., 2001). The characteristics of LD become more evident during school learning, yet its manifestations may occur earlier. Metacognitive strategies are more effective tools in helping students with dyscalculia to acquire the skills and methods to solve mathematical problems. It is nowadays widely accepted that metacognitive knowledge and skills influence mathematical problem solving (e.g., Borkowski, Chan, & Muthukrishna, 2000). Inprasitha (2003) in his study found that when students read mathematical problems, they knew what were given in the questions, but they could solve problems only to a certain extent. As for metacognitive strategies, students conducted observation and investigation before problem-solving by developing plans, monitoring, and evaluating their own learning or thinking, this approach improved student’s efficiency in open-ended problem-solving. Metacognitive strategies can bring about successful student mathematical problem-solving. There is increasing interest on the roles of metacognition in mathematical problem solving. However, little is known about the nature of elementary student’s use of metacognitive strategies, and how these strategies are applied when students solve problems.

Metacognitive strategies positively impact students who have learning problems because they provide these students an efficient way to acquire, store, and express information and skills (Mercer & Mercer, 1993). For many students who have learning problems, their inability to efficiently retrieve information previously stored in memory negatively impacts their ability to accurately express what they know. Well developed metacognitive strategies aide such information retrieval for these students. Students who have learning problems tend to be passive learners. While the reasons for this learning characteristic may differ based on students’ individual learning problems (e.g. memory problems, cognitive processing difficulties, learned helplessness), effective metacognitive strategies can be of substantial benefit to students who have a variety of learning problems.

Strategies should be directly taught to students who have learning problems. The use of explicit teacher modeling is the most effective way to ensure that these students will understand the purpose of a metacognitive strategy, how to use it, and under what circumstances it should be used (Lenz, Ellis, & Scanlon, 1996). Providing students with practice opportunities using the metacognitive strategy is also an important component of metacognitive strategy instruction. It is also very helpful to provide students visual cues of the strategy in the classroom.

The key to the success of metacognitive strategies is that when they are taught appropriately, they assist learners who are dependent on high levels of teacher support to become independent learners. When students have been directly taught the strategy, the strategy’s purpose, how to use the strategy, and are provided opportunities to practice using the strategy, these students posses a powerful learning tool that builds learning independence. Confronted with a problem-solving situation, these students can now implement the appropriate metacognitive strategy when they have difficulty remembering how to solve a particular problem. Therefore, instead of relying on the teacher for assistance, they can independently help themselves. This can be a tremendously invigorating feeling for students and teachers.